1. Field of the Invention
This invention relates to the measurement of small currents using a transimpedance amplifier. The present invention teaches a method to create a transimpedance amplifier that has wide bandwidth and very high linearity.
2. Description of the Prior Art
FIG. 1 shows a common transimpedance amplifier circuit used to measure small currents know as an IV converter. Referring to FIG. 1, an IV converter 10 consists of an operational amplifier U1, a feedback resistor Ro, and a feedback capacitance Cf U1 has a non-inverting terminal V+, an inverting terminal Vxe2x88x92, and an output terminal Vout. Ro is connected between Vout and Vxe2x88x92 so that Ro provides negative feedback around U1. Cf is connected in parallels with Ro and represents the sum of the stray capacitance across Ro together with any additional feedback capacitance that parallels Ro. An input current Isrc 5 that is to be measured is connected to Vxe2x88x92. Thus Vxe2x88x92 serves as the transimpedance input. V+ is connected to ground. Since U1 has a very large open loop gain, negative feedback forces Vxe2x88x92 to act as a low impedance virtual ground, and all of Isrc 5 flows across Ro. IV converter 10 produces an output voltage Vout given by:
Vout=xe2x88x92IsrcRo(E1)
when Cf is small enough to be ignored. Thus Vout serves as the transimpedance output. Therefore IV converter 10 measures an input current by producing an output voltage proportional to the input current. The constant of proportionality is called the transimpedance, and IV converter 10 the transimpedance is equal to the feedback resistance Ro.
An important property of IV converter 10 is the low input impedance it presents to Isrc 5. This low input impedance isolates Isrc 5 from voltage changes that would otherwise occur due to changing input current. An application requiring such a low input impedance is the linear measurement of photodiode current. Most photodiodes exhibit a nonlinear response with changes in bias voltage. The low input impedance of IV converter 10 ensures that the photodiode bias voltage remains constant, regardless of the value of photodiode current flowing. Another application requiring low input impedance is voltage clamping ionic currents in biological preparations. The low input impedance of IV converter 10 enables it to be conveniently used as biological voltage clamp (see Electronic Design of the Patch Clamp by F. J. Sigworth, 1983, found in Single-Channel Recording, edited by B. Sakmann and E. Neher, 1983). When used as a biological voltage clamp, V+ of U1 is driven by a command voltage instead of being grounded as in FIG. 1, and Isrc 5 is commonly a single cell under patch clamp conditions. The low input impedance of IV converter 10 ensures the cell is voltage clamped at the command voltage.
As with any amplifier, IV converter 10 has an inherent signal-to-noise ratio (SNR) that limits the minimum size input signal that can be detected; to measure small currents it is necessary to maximize the SNR. The dominant noise source that degrades the SNR of IV converter 10 is the thermal Johnson noise of the feedback resistor Ro. The root-mean-square SNR for a given input signal Isrc in the presence of the thermal noise of Ro is given by                               SNR          rms                =                              I            src                    ⁢                      c            1                    ⁢                                    R              o                                                      R                o                                                                        (        E2        )            
where c1 is a function of the measurement bandwidth and temperature.
As can be seen from Eq. E2, larger values of Ro improve the SNR since the numerator of Eq. E2 grows faster than the denominator as Ro is increased. When IV converter 10 is used to measure small currents such as those produced by a photodiode or a biological preparation, large values of Ro must be used to ensure adequate SNR; typical values of Ro range from tens of Megaohms to GigaOhms. When such high Ro values are used, the effects of Cf can no longer be ignored. These effects are quantified by the transfer function of Isrc 5 to Vout, given by                                           V            out                                I            src                          =                              -                          R              o                                                                          R                o                            ⁢                              C                f                            ⁢              s                        +            1                                              (        E3        )            
where s is the Laplace transform frequency variable. As shown in Eq. E3, Cf in parallel with Ro combine to create a pole with time constant xcfx84uncomp=RoCf which rolls off the frequency response. When Ro is large, xcfx84uncomp becomes large enough to degrade the measurement bandwidth. While xcfx84uncomp can be decreased by physically lowering Cf, stability requirements preclude lowering Cf much below 5 pF. To ensure stability of IV converter 10, it is generally necessary that Cf be on the order of the input capacitance at the inverting terminal Vxe2x88x92 to avoid gain peaking (see Designing Photodiode Amplifier Circuits with OPA 128, Burr Brown Application Bulletin, 2000) Therefore, IV converter 10 usually has a signal bandwidth limit of xcx9c1kH or less when measuring small currents, which is undesirable.
In order to increase the bandwidth of IV converter 10, it is common practice to use a post-amplification equalizer, as shown in FIG. 1. Referring to FIG. 1, a post-amplification equalizer 20 takes as input Vout and produces an output voltage Vout_equ 25. Equalizer 20 serves to cancel the pole in equation E3 by introducing a real left-hand plane zero with time constant xcfx84zero=xcfx84uncomp, In this way, equalizer 20 increases the output bandwidth of IV converter 10.
While equalizer 20 does increase bandwidth, it has several practical limitations stemming from the need to achieve and then to maintain accurate pole-zero cancellation. To achieve cancellation, equalizer 20 must be manually tuned for each IV converter produced because xcfx84uncomp varies with the parameter spread of Ro and Cf. This tuning adds significant expense to large volume productions. More significantly, maintaining accurate cancellation is difficult since xcfx84uncomp and xcfx84zero drift unequally with changes in ambient temperature and humidity. The result of incomplete cancellation is the introduction of nonlinearities in the frequency response of IV converter 10 within the signal measurement bandwidth. Even with stable components, the accuracy of cancellation is degraded at higher frequencies owing to the well-know difficulties in making broadband analog equalizers.
A linear frequency response of IV converter 10 is especially important when voltage clamping ionic currents from single cell preparations using the whole-cell patch clamp technique. Under these conditions Vout is used as positive feedback to compensate for the high impedance of the measuring electrode using a technique called series resistance compensation (see Sigworth pages 28 to 32). As outlined by Sigworth, nonlinearities in the frequency response of IV converter 10 destabilizes series resistance compensation. Linear frequency response is also required when implementing series resistance compensation using a membrane state estimator, as taught by Sherman in U.S. Pat. No. 6,163,719 (2000). (See also Sherman et. al. 1999. Series Resistance Compensation for Whole-Cell Patch-Clamp Studies Using a Membrane State Estimator, Biophys. J. 77:2590-2601.). Consequently, it is extremely difficult to implement wideband series resistance compensation when using an IV converter equipped with a post-amplification equalizer.
In order to increase bandwidth, other transimpedance amplifier architectures are used which, unlike the IV converter, present a relatively high input impedance to the input current source. Rodgers (U.S. Pat. No. 5,982,232 (1999)) teaches a technique wherein the bandwidth of a high input impedance transimpedance amplifier is increased by using positive capacitive feedback to reduce the effects of input capacitance loading. While high bandwidths can be achieved using this technique, the high input impedance precludes its use in the many applications that require a low input impedance.
In summary, while the IV converter is a low noise, low input impedance transimpedance amplifier well-suited to the measurement of small currents, its low measurement bandwidth is a significant drawback. The practice of using an equalizer to improve the measurement bandwidth has the following disadvantages:
a. The equalizer must be manually tuned, increasing production cost.
b. Parameter variations with temperature and humidity make it difficult for the equalizer to maintain accurate pole-zero cancellation, thus compromising performance.
c. It is difficult for the equalizer to maintain accurate pole-zero cancellation over broad frequencies, thus introducing nonlinearities in the measurement bandwidth.
Accordingly, several objects and advantages of the present invention are:
a. to provide a wide bandwidth transimpedance amplifier that does not require manual tuning;
b. to provide a wide bandwidth transimpedance amplifier that is independent of parameter changes; and
c. to provide a wide bandwidth transimpedance amplifier with high linearity.